Hopefully someone can help me out. I don't understand how to get higher rank fieldcraft leves. I'm a rank 15 miner and can only access the rank 20 mining leves from my hometown of Limsa. When I go to the other cities to do mining leves the highest mining fieldcraft leves that show up are rank 10. I can access rank 20 battle leves with a rank 8 pugilist but can't get rank 20 mining leves as a rank 15 miner. How do I get access to the rank 20 fieldcraft leves?

My bet is on "wait until retail". Everything you're doing now to progress your character will be meaningless in two days, and there's no point speculating/hypothesizing what you might need to do to get higher rank leves in other cities because for all we know, SE designed it that way to keep a lid on DoL progression through the beta. Who knows? Maybe you need to do a certain number of rank 1/10 fieldcraft leves with a given city before you can get rank 20 leves. Maybe the random goat decided the other cities weren't going to have any rank 20 leves for you this time around.

Yes, as Sephrick said, you have to visit and access the Aethyrte of the lv 20 camp at least once(in teleport list), before you get access to the leve there. Lominsa i assume is Camp BloodShore. This is because you need "grade 3" mining point for the leve and it is only available near the camp.